4-D Location of Observers

A blue guy and a red guy are moving at the same speed in opposite directions with respect to some rest system as depicted in the sketch below. Both guys are moving into their respective 4th dimensions at light speed. The same proper time has lapsed for blue and red at their respective events labled "B" (for blue) and "R2" (for red). But, when Blue is at his "B" event, his 3-dimensional "Blue World" includes Red at red's "R1" event.

Question: Which 3-D world (Red World1 or Red World 2) is the Red guy physically really living in at the time blue is living in his "Blue World" containing event "B"?

Question: Which 3-D world (Red World1 or Red World 2) is the Red guy physically really living in at the time blue is living in his "Blue World" containing event "B"?

Hmm, we have such precisely defined physical concepts as the 3-d world someone is "really living in". I don't know about you, but I experience what my senses tell me at one location at a given moment. All else is interpreted relative to a (hopefully useful but not directly verifiable) model.

By typical simulaneity definition, red at R2 considers B in his future. However, by the notion of "conventionality of simultaneity", red at R2 may consider any event with spacelike interval as simultaneous with R2. The red at R2 can pick any event from Blue a bit before your "red world 2" crosses the blue world line until well after B as simultaneous.

Another phrasing of this idea, is: any part of B's worldline which can neither be influenced by R2 nor influence R2, is causally disconnected such that not only statements about simultaneity but even existence are unknowable hypotetheses.

Just another obvious comment: per standard simultaneity convention, B says R2 is in its future, R2 says B is in its future, and this is a perfectly normal statement in the context of relativity of simultaneity.

I'm going to try to make the question a little more specific. A third observer is thrown into the mix--the Brown guy. His event, "Brn", coincides with the blue event, "B". They both have the Red guy in their respective 3-D worlds at that instant in time.

So now, which 3-D world is Red living in at the time of the shared event "B" and "Brn", Red World 1 or Red World 2?

I'm going to try to make the question a little more specific. A third observer is thrown into the mix--the Brown guy. His event, "Brn", coincides with the blue event, "B". They both have the Red guy in their respective 3-D worlds at that instant in time.

So now, which 3-D world is Red living in at the time of the shared event "B" and "Brn", Red World 1 or Red World 2?

It doesn't change anything. If R takes the minimalist perspective, they say anything outside their light cones at R2 is unknowable, unknown simultaneity (for all R knows at R2, Blue and brown are anti-particles, and changed direction to annihilate before the B/Brn event (on their world lines). If R takes the conventional Lorentz simultaneity convention, R2 is the simultaneity surface. B is in R2's future, and the presence of Brn at the same event has no relevance. So, with the Lorentz convention, Brn says R2 and B/Brn are simultaneous, B says R2 is in the future of B/Brn, R2 says B/Brn is in its future. Again, this is all normal.

Within the limitation that a simultaneity convention relates spacelike events, there are many other possible conventions, some producing 'nicer' results for comparing a hypothetical rocket log with earth log after a rocket returns to earth (i.e. they are smoother in the presence of sharp accelerations). However, if these are used to build coordinates, the things like Maxwell's equations take a more complex form even in the inertial portions of a rocket round trip.

While philosophical questions (such as what's really real) don't necessarily have a definite, scientific answer, I personally think it's simplest to think of the red observer's "now" as defined by the red lines of simultaneity, and the blue observer's now as defined by the blue lines, etc.

As you have already noticed, they all have different notions of "now', because simultaneity is relative.

(And congratulations for noticing this, we get a lot of confused posts from people who haven't realized this yet.)

This fits in nicely with a philsophical assumption that "now" is a mental construct. It's not precisely relevant, but for human beings, "now" is synthesized from sensory signals from various sources that arive at different times with different delays, which are interpreted into a unified picture of the world as a mental picture of "now".

The mental picture is always out of date, it takes some time to process the sensory data to come up with the mental model. This leads to phenomenon such as reaction time.

A related philsophical point is that the Lorentz interval is not observer dependent, so it's sometimes convienient to regard it as "really real". "really real" is sort of vague, "observer independent" is more precise, but if you divide the mental landscape into observer dependent things, and observer independent things, space and time fall in the category of observer dependent things, and the Lorentz interval (at least according to Special relativity) falls in the category of observer independent things.

I find it convenient to regard the observer independent things as being "really real", then I don't need to consider an observer unless one is needed. This approach won't necessarily work for quantum mechanics, but it's convenient for classical mechanics.

While philosophical questions (such as what's really real) don't necessarily have a definite, scientific answer, I personally think it's simplest to think of the red observer's "now" as defined by the red lines of simultaneity, and the blue observer's now as defined by the blue lines, etc.

As you have already noticed, they all have different notions of "now', because simultaneity is relative.

(And congratulations for noticing this, we get a lot of confused posts from people who haven't realized this yet.)

This fits in nicely with a philsophical assumption that "now" is a mental construct. It's not precisely relevant, but for human beings, "now" is synthesized from sensory signals from various sources that arive at different times with different delays, which are interpreted into a unified picture of the world as a mental picture of "now".

The mental picture is always out of date, it takes some time to process the sensory data to come up with the mental model. This leads to phenomenon such as reaction time.

A related philsophical point is that the Lorentz interval is not observer dependent, so it's sometimes convienient to regard it as "really real". "really real" is sort of vague, "observer independent" is more precise, but if you divide the mental landscape into observer dependent things, and observer independent things, space and time fall in the category of observer dependent things, and the Lorentz interval (at least according to Special relativity) falls in the category of observer independent things.

I find it convenient to regard the observer independent things as being "really real", then I don't need to consider an observer unless one is needed. This approach won't necessarily work for quantum mechanics, but it's convenient for classical mechanics.

Thanks for a very nice discussion. I can't disagree with anything you or PAllen have said.

I agree with what PAllen and pervect have said. I'll just pick up on one point:The phrase "...at the time..." only makes sense if you have already decided on what "simultaneity" means, so it's just as coordinate-dependent as everything else already mentioned.

P.S. It's a good idea to keep embedded images reasonable small -- wide images cause problems for people trying to read the thread in a small window.

Good point, DrGreg. And thanks for the pointers on the graphics. I was not happy with taking up all of that screen space. That's the problem with using Paint *.bmp files. I'll have to get familiar with PNG.

I appreciate the points about the coordinate dependency of simultaneity and the future and past events. And, again, I certainly agree with all of the points raised in the above posts.

After reflecting on the above responses it leaves me wondering if, in the view of most physicists (and I regard you folks as doing a pretty good job of representing views of physicists), special relativity does not allow us to make a statement (referring to my example) about what 3-D world Red is living in when Blue and Brown share the event "B" and "Brn". Perhaps you feel physics cannot say what 3-D world Red is "really" living in (and here I'm referring to Red's 3-D World 1 and/or World 2--not just the event R1 or R2).

This is all very philosphic, but I would say it is reasonable for an inertial observer in sufficiently flat spacetime to think in terms of Lorentz simultaneity:...

I certainly agree that we must set up our problem based on an unmistakeable consistency with special relativity (for flat spacetime, as you point out). Once we have the basic physics right, then we can consider possible physical implications, within the context of physics rather than philosophy.

When a spacecraft is in orbit on the opposite side of the moon (and no communication), we don't hesitate to talk about what is going on with the satellite in physical terms (it is "really" out there). We speak about what binary stars are doing without fear of being philosophical.We've even become accustomed to speaking about the Big Bang without trepidation. We exchange ideas on aspects of black holes without thinking of ourselves as being too philosophical for physics.

So, it would not seem too far afield to inquire about any physical implications of problem situations set up in the context of Minkowski space, provided we have not corrupted the fundamental theory of special relativity.

That's the spirit in which, from time to time (actually, for years since grad school days) I like to inquire once again about where observers or objects physically reside in the context of the spacetime diagrams, and in the context of physics rather than philosophy.

If they are following the red world line, then at R2 they 'live' you red world 2. The red world they live in that includes the B/Brn event is one well in the future of R2.

Thanks for pointing out one more 3-D world (Red World 3 in the diagram below) that should be included for consideration. So, we have the blue guy seeing Red at "R1" at the same time the Brown guy sees Red at "R2", while Red sees Blue and Brown at "B"/"Brn" when Red is at "R3". (please avoid complications of accounting for delays associated with light transmission--we are concerned with the inertial frames).

Can we say anything about the 3-D world Red occupies in this scenario?

We can add in a companion to the Red observer. We add in the Red companion's world line; it shares the event that is also shared by the Blue and Brown guys at "B"/"Brn".

So, now we can imagine a brief exchange of comments between the three guys as they pass each other at the "B"/"Brn"/BlueCompanion event. Blue says, "Hey, I have the Red guy in my 3-D World at event R1." Brown says, "No way. I have him in my 3-D World at event R2." The Red guy's companion (who has been stationed at some distance along Red's X1 axis) says, "You guys are nuts. My Red boss gave me instructions to wait out here until I meet up with you guys to let you know that I have my Red boss in my 3-D Red World 3, and he is at event R3 even as we speak--even though you guys won't even see event R3 until some time into your future (as suggested by PAllen).

But wait--which one of these three guys is correct? How can Red be in all three places at the same time as Blue, Brown and Red Companion meet?

I certainly agree that we must set up our problem based on an unmistakeable consistency with special relativity (for flat spacetime, as you point out). Once we have the basic physics right, then we can consider possible physical implications, within the context of physics rather than philosophy.

When a spacecraft is in orbit on the opposite side of the moon (and no communication), we don't hesitate to talk about what is going on with the satellite in physical terms (it is "really" out there). We speak about what binary stars are doing without fear of being philosophical.We've even become accustomed to speaking about the Big Bang without trepidation. We exchange ideas on aspects of black holes without thinking of ourselves as being too philosophical for physics.

So, it would not seem too far afield to inquire about any physical implications of problem situations set up in the context of Minkowski space, provided we have not corrupted the fundamental theory of special relativity.

That's the spirit in which, from time to time (actually, for years since grad school days) I like to inquire once again about where observers or objects physically reside in the context of the spacetime diagrams, and in the context of physics rather than philosophy.

You are mixing several types of things here. The only one similar to you diagram is speculating on what is happening 'now' on a satellite on the other side of the moon. Most of the others are cases of talking about past events that are causally connected to us (including the big bang - which is in the causal past of the whole universe). I would say it is rather bold to talk about the current status of something a billion light years away, where the last information we have of it is a billion years old. As for black holes, we observe a number of objects believed to be well approximated by the GR model of black holes. I believe most physicists do not believe these objects are exactly described by GR black holes.

As for the satellite, while there may significant signal delays, relativistic corrections to clock rates and simultaneity are so small it would take a high precision experiment looking for them to see a small effect. So one can get away with an image of 'distant now'.

Thanks for pointing out one more 3-D world (Red World 3 in the diagram below) that should be included for consideration. So, we have the blue guy seeing Red at "R1" at the same time the Brown guy sees Red at "R2", while Red sees Blue and Brown at "B"/"Brn" when Red is at "R3". (please avoid complications of accounting for delays associated with light transmission--we are concerned with the inertial frames).

Can we say anything about the 3-D world Red occupies in this scenario?

I would say it is reasonable to say that at R3, red world line observer is 'really occupying' red world 3.

We can add in a companion to the Red observer. We add in the Red companion's world line; it shares the event that is also shared by the Blue and Brown guys at "B"/"Brn".

So, now we can imagine a brief exchange of comments between the three guys as they pass each other at the "B"/"Brn"/BlueCompanion event. Blue says, "Hey, I have the Red guy in my 3-D World at event R1." Brown says, "No way. I have him in my 3-D World at event R2." The Red guy's companion (who has been stationed at some distance along Red's X1 axis) says, "You guys are nuts. My Red boss gave me instructions to wait out here until I meet up with you guys to let you know that I have my Red boss in my 3-D Red World 3, and he is at event R3 even as we speak--even though you guys won't even see event R3 until some time into your future (as suggested by PAllen).

But wait--which one of these three guys is correct? How can Red be in all three places at the same time as Blue, Brown and Red Companion meet?

They're all correct by useful convention. By the minimalist philosophy I alluded to in earlier posts, they instead say we know nothing about distant now. Instead, at B/Brn/Rcompanion event, they look what time they see on Red's clock - and they all agree (a bit before R1). All else is convention.

Now the standard convention is very useful for inertial observers in flat spacetime because all reasonable ways of measuring simultaneity agree on it. In particular, at the B/Brn event, if all 3 do as follows:

Given the history of what each has seen from red, including speed determined from doppler, distance measured in the past by any reasonable method (radar ranging, parallax, etc.), each computes what time should be on red's clock 'now' (the B/Brn event), each of the 3 will insist on a different answer. How could you possibly say one is right? Each is right for their state of motion, under a reasonable model.

You are mixing several types of things here. The only one similar to you diagram is speculating on what is happening 'now' on a satellite on the other side of the moon. Most of the others are cases of talking about past events that are causally connected to us (including the big bang - which is in the causal past of the whole universe). I would say it is rather bold to talk about the current status of something a billion light years away, where the last information we have of it is a billion years old. As for black holes, we observe a number of objects believed to be well approximated by the GR model of black holes. I believe most physicists do not believe these objects are exactly described by GR black holes.

As for the satellite, while there may significant signal delays, relativistic corrections to clock rates and simultaneity are so small it would take a high precision experiment looking for them to see a small effect. So one can get away with an image of 'distant now'.

I would say it is reasonable to say that at R3, red world line observer is 'really occupying' red world 3.

I certainly agree with that statement, at R3, Red is 'really occupying' Red World 3.

However, at R2, Red is 'really occupying' Red World 2. And at R1, Red is 'really occupying' Red World 1.

So, as Blue, Brown and RedCompanion compare notes, how do they resolve the question of which of the worlds Red is actually living in at the time they are meeting (although such a brief meeting!): Red World 1, Red World 2, or Red World 3?

Staff: Mentor

Does this discussion have anything to do with the so-called Block Universe concept?

You're relatively new to the forum here, Chestermiller, so, welcome! Thanks for jumping in. And that is a very astute observation you've made. Perhaps you go to the head of the class with that one.

Upon reflection of your observation it is quite clear that you are on the mark. I've been reading quite a bit about block universe since your post, refreshing my memory and finding literature new to me. The Red guy in the space-time diagrams above manifestly exists in all three of the 3-D worlds--all at once (Red World 1, Red World 2, and Red World 3): A classic example of block universe. You see a similar picture of the block universe with Roger Penrose's famous "Andromeda Galaxy Paradox."

Since Kurt Godel's work in the late 40's and early '50's, there seems to have been a growing recognition among physicists that the block universe is indeed directly implied by special relativity (and general relativity). It's not the philosophy so much as opening the window into the understanding of the foundations of physics. And there follows then several powerful implications about how nature is operating.

Philosophers have picked up the trail at this point and gone off in their own directions--but as physicists we don't care to pay much attention to what they are up to.

The tradition of physics involves pursuing questions about what is out there, independent of observers and thinkers, and what rules account for the observed phenomena. The block universe concept appears to be fundamental in this context. And in the end, it is only part of physics if it is backed up by measurements.

Whether the 4-dimensional block universe will be expanded to include the additional dimensions of string theory remains to be seen.